Properties

Level $1$
Weight $0$
Character 1.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 39.773622619 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.605601238\) \(a_{3}=-1.350325009\) \(a_{4}=+1.577955337\) \(a_{5}=+1.541245692\)
\(a_{6}=-2.168083506\) \(a_{7}=-0.295682907\) \(a_{8}=+0.927965805\) \(a_{9}=+0.823377629\) \(a_{10}=+2.474625992\)
\(a_{11}=+0.163502595\) \(a_{12}=-2.130752554\) \(a_{13}=+0.342120955\) \(a_{14}=-0.474748842\) \(a_{15}=-2.081182602\)
\(a_{16}=-0.088012291\) \(a_{17}=+1.077391499\) \(a_{18}=+1.322016141\) \(a_{19}=+0.580121303\) \(a_{20}=+2.432016891\)
\(a_{21}=+0.399268024\) \(a_{22}=+0.262519969\) \(a_{23}=+0.002384987\) \(a_{24}=-1.253055433\) \(a_{25}=+1.375438283\)
\(a_{26}=+0.549309828\) \(a_{27}=+0.238497604\) \(a_{28}=-0.466574422\) \(a_{29}=+1.163388046\) \(a_{30}=-3.341549364\)
\(a_{31}=+1.377885496\) \(a_{32}=-1.069278449\) \(a_{33}=-0.220781643\) \(a_{34}=+1.729861126\) \(a_{35}=-0.455720007\)
\(a_{36}=+1.299253124\) \(a_{37}=+1.627261560\) \(a_{38}=+0.931443486\) \(a_{39}=-0.461974481\) \(a_{40}=+1.430223299\)
\(a_{41}=+0.962830243\) \(a_{42}=+0.641065235\) \(a_{43}=-0.937336394\) \(a_{44}=+0.257999792\) \(a_{45}=+1.269027224\)
\(a_{46}=+0.003829338\) \(a_{47}=-0.473766106\) \(a_{48}=+0.118845198\) \(a_{49}=-0.912571618\) \(a_{50}=+2.208405410\)
\(a_{51}=-1.454828686\) \(a_{52}=+0.539851586\) \(a_{53}=-0.630908602\) \(a_{54}=+0.382932049\) \(a_{55}=+0.251997670\)
\(a_{56}=-0.274383627\) \(a_{57}=-0.783352306\) \(a_{58}=+1.867937287\) \(a_{59}=+0.227386385\) \(a_{60}=-3.284013195\)
\(a_{61}=+1.094242639\) \(a_{62}=+2.212334659\) \(a_{63}=-0.243458691\) \(a_{64}=-1.628822511\) \(a_{65}=+0.527292447\)
\(a_{66}=-0.354487276\) \(a_{67}=-0.494610723\) \(a_{68}=+1.700075692\) \(a_{69}=-0.003220508\) \(a_{70}=-0.731704608\)
\(a_{71}=-0.609026792\) \(a_{72}=+0.764066284\) \(a_{73}=-1.517479789\) \(a_{74}=+2.612733175\) \(a_{75}=-1.857288711\)
\(a_{76}=+0.915405509\) \(a_{77}=-0.048344923\) \(a_{78}=-0.741746799\) \(a_{79}=+0.682201987\) \(a_{80}=-0.135648565\)
\(a_{81}=-1.145426909\) \(a_{82}=+1.545921430\) \(a_{83}=-1.044632622\) \(a_{84}=+0.630027110\) \(a_{85}=+1.660525007\)
\(a_{86}=-1.504988476\) \(a_{87}=-1.570951973\) \(a_{88}=+0.151724817\) \(a_{89}=+0.343826726\) \(a_{90}=+2.037551682\)
\(a_{91}=-0.101159319\) \(a_{92}=+0.003763403\) \(a_{93}=-1.860593244\) \(a_{94}=-0.760679447\) \(a_{95}=+0.894109462\)
\(a_{96}=+1.443873431\) \(a_{97}=-0.138134314\) \(a_{98}=-1.465226121\) \(a_{99}=+0.134624379\) \(a_{100}=+2.170380179\)

Showing 100 of 5000 available coefficients

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